A controlled one and two atom cavity system [Elektronische Ressource] / vorgelegt von Mkrtych Khudaverdyan
100 Pages
English

A controlled one and two atom cavity system [Elektronische Ressource] / vorgelegt von Mkrtych Khudaverdyan

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A controlled one and twoatom-cavity systemDissertationzurErlangung des Doktorgrades (Dr. rer. nat.)derMathematisch-Naturwissenschaftlichen FakultätderRheinischen Friedrich-Wilhelms-Universität Bonnvorgelegt vonMkrtych KhudaverdyanausMoscow (Russia)Bonn 2009Angefertigt mit Genehmigung der Mathematisch-Naturwissenschaftlichen Fakultätder Rheinischen Friedrich-Wilhelms-Universität Bonn1. Referent: Prof. Dr. Dieter Meschede2.t: Prof. Dr. Martin WeitzTag der Promotion: 15.09.2009AbstractIn this thesis I present an experimental realization of controlled systems consisting oftrapped neutral atoms strongly coupled to a high-finesse optical resonator. These systemsenable the exploration of atom-light interaction at the most fundamental level, and havea potential application in quantum information processing.Experimental tools for preparation, detection and transport of individual Caesiumatoms into the cavity mode are presented. In addition, the setup and properties of theresonator are discussed.I investigate two different methods to detect the atom-cavity interaction. The firstapproach relies on the observation of the cavity transmission, which allows us to contin-uously monitor the interaction dynamics of a single atom coupled to the resonator modefor several seconds. Using this approach I characterize the system and investigate thedependence of the coupling strength on the number of atoms and their position inside thecavity mode.

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Published 01 January 2009
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A controlled one and two
atom-cavity system
Dissertation
zur
Erlangung des Doktorgrades (Dr. rer. nat.)
der
Mathematisch-Naturwissenschaftlichen Fakultät
der
Rheinischen Friedrich-Wilhelms-Universität Bonn
vorgelegt von
Mkrtych Khudaverdyan
aus
Moscow (Russia)
Bonn 2009Angefertigt mit Genehmigung der Mathematisch-Naturwissenschaftlichen Fakultät
der Rheinischen Friedrich-Wilhelms-Universität Bonn
1. Referent: Prof. Dr. Dieter Meschede
2.t: Prof. Dr. Martin Weitz
Tag der Promotion: 15.09.2009Abstract
In this thesis I present an experimental realization of controlled systems consisting of
trapped neutral atoms strongly coupled to a high-finesse optical resonator. These systems
enable the exploration of atom-light interaction at the most fundamental level, and have
a potential application in quantum information processing.
Experimental tools for preparation, detection and transport of individual Caesium
atoms into the cavity mode are presented. In addition, the setup and properties of the
resonator are discussed.
I investigate two different methods to detect the atom-cavity interaction. The first
approach relies on the observation of the cavity transmission, which allows us to contin-
uously monitor the interaction dynamics of a single atom coupled to the resonator mode
for several seconds. Using this approach I characterize the system and investigate the
dependence of the coupling strength on the number of atoms and their position inside the
cavity mode. An alternative method, providing information on the atom-field interaction,
is based on the detection of the atomic state. We use this method to record the spectrum
of the interacting single-atom-cavity system, which reveals the vacuum Rabi splitting - a
clear signature of coherent atom-field interaction in the strong coupling regime. Exploiting
the strong interaction in combination with the large energy separation between the spin
states of Caesium atoms, a projective quantum nondemolition measurement of the atomic
spin state is performed. Continuous monitoring of the atomic state reveals quantum jumps
between the states. By extending the experiment to the case of two atoms simultaneously
coupled to the cavity mode, conditional dynamics of the spin states is observed. By further
advancing this method, generation and detection of entangled states might be feasible.
Parts of this thesis have been published in the following journal articles:
1. M. Khudaverdyan, W. Alt, I. Dotsenko, T. Kampschulte, K. Lenhard, A. Rauschen-
beutel, S. Reick, K. Schörner, A. Widera and D. Meschede Controlled insertion and
retrieval of atoms coupled to a high-finesse optical resonator, NewJ.Phys. 10, 073023
(2008)
2. M. Khudaverdyan, W. Alt, T. Kampschulte, S. Reick, A. Thobe, A. Widera and
D. Meschede Quantum jumps and conditional spin dynamics in a strongly coupled
atom-cavity system, Phys. Rev. Lett. 103, 123006 (2009)Contents
Abstract V
Introduction 1
1 Experimental setup 3
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2 Cooling and trapping single atoms . . . . . . . . . . . . . . . . . . . . . . . 3
1.2.1 Magneto-optical trap – a source of single neutral atoms . . . . . . . 3
1.2.2 Optical dipole trap – a conveyor belt for atoms . . . . . . . . . . . . 6
1.2.3 Fluorescence detection and imaging of single atoms . . . . . . . . . . 18
1.2.4 Transportation and position control . . . . . . . . . . . . . . . . . . 20
1.3 A high-finesse optical resonator . . . . . . . . . . . . . . . . . . . . . . . . . 21
1.3.1 Mechanical setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
1.3.2 Stabilizing the resonance frequency of the cavity . . . . . . . . . . . 25
1.3.3 Transmission detection . . . . . . . . . . . . . . . . . . . . . . . . . . 28
2 Atom-cavity system in the strong coupling regime 31
2.1 The Jaynes-Cummings model . . . . . . . . . . . . . . . . . . . . . . . . . . 32
2.2 The master equation approach . . . . . . . . . . . . . . . . . . . . . . . . . 34
2.3 Detection of atom-cavity coupling via cavity transmission . . . . . . . . . . 37
2.3.1 Detection of a single atom inside the cavity . . . . . . . . . . . . . . 37
2.3.2 Simple model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
2.3.3 Dynamics of the atom-cavity coupling strength . . . . . . . . . . . . 41
2.3.4 Controlling the coupling strength . . . . . . . . . . . . . . . . . . . . 45
2.3.5 Atom-number dependent coupling strength . . . . . . . . . . . . . . 45
2.4 Detection of atom-cavity coupling via the atomic state . . . . . . . . . . . . 48
2.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
3 Quantum jumps and normal mode splitting 51
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
3.2 Quantum jumps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
3.2.1 Intra-cavity quantum nondemolition (QND) detection of the atomic
state . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
3.2.2 A random telegraph signal of quantum jumps . . . . . . . . . . . . . 54
3.2.3 Characterization of quantum jumps . . . . . . . . . . . . . . . . . . . 55
3.2.4 Towards quantum jumps with more than one atom . . . . . . . . . . 61
3.3 Measuring the normal mode splitting via the atomic state . . . . . . . . . . 65
3.3.1 Experimental sequence . . . . . . . . . . . . . . . . . . . . . . . . . . 65
3.3.2 Stability of the coupling strength . . . . . . . . . . . . . . . . . . . . 67
3.3.3 Measurement of the normal-mode splitting via the atomic state . . . 72
3.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
VIIVIII CONTENTS
Conclusion and Outlook 76
Bibliography 81
Acknowledgements 89List of Figures
1.1 Principle of Doppler cooling . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.2 of the MOT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.3 Relevant energy levels of Cs atom . . . . . . . . . . . . . . . . . . . . . . . . 7
1.4 Standing wave dipole potential . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.5 Microscope image of the step-index fiber . . . . . . . . . . . . . . . . . . . . 10
1.6 Measurement of the polarization properties of the fiber . . . . . . . . . . . . 12
1.7 Quality of the laser beam of the fiber-based DT . . . . . . . . . . . . . . . . 14
1.8 Position fluctuation of the DT laser beam . . . . . . . . . . . . . . . . . . . 16
1.9 Measurement of the atomic oscillation frequencies inside the DT. . . . . . . 17
1.10 Experimental setup and detection optics . . . . . . . . . . . . . . . . . . . . 19
1.11 Fluorescence CCD image of a single atom stored inside the DT . . . . . . . 20
1.12 Schematic of the cavity mirror . . . . . . . . . . . . . . . . . . . . . . . . . . 21
1.13 Geometrical configuration of cavity, MOT, and DT. . . . . . . . . . . . . . . 23
1.14 Schematics of the cavity holder . . . . . . . . . . . . . . . . . . . . . . . . . 24
1.15 Frequency stabilization of the high-finesse cavity . . . . . . . . . . . . . . . 26
1.16 Lifetime of atoms inside the cavity mode . . . . . . . . . . . . . . . . . . . . 27
1.17 Sketch of the detection setup . . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.1 Energy levels in the Jaynes-Cummings model . . . . . . . . . . . . . . . . . 32
2.2 map in the Ja model . . . . . . . . . . . . . . . . . . 34
2.3 Dressed states of the atom-cavity system in master equation approach . . . 36
2.4 Continuous strong coupling of a single atom to the cavity field . . . . . . . . 38
2.5 Probe and lock laser intra-cavity standing waves . . . . . . . . . . . . . . . 40
2.6 Dynamics of a single atom coupling to the cavity field . . . . . . . . . . . . 42
2.7 and equilibrium of a single atom-field coupling . . . . . . . . . . . 43
2.8 Sisyphus-type intra-cavity cooling . . . . . . . . . . . . . . . . . . . . . . . . 44
2.9 Controlling the atom-cavity coupling . . . . . . . . . . . . . . . . . . . . . . 46
2.10 Atom-number dependent strength . . . . . . . . . . . . . . . . . . 47
2.11 Detecting the atom-cavity coupling via the final atomic state . . . . . . . . 48
3.1 Nondemolition intracavity detection of the atomic state . . . . . . . . . . . 53
3.2 Demonstration of quantum jumps . . . . . . . . . . . . . . . . . . . . . . . . 55
3.3 Histogram of transmission counts for quantum jumps . . . . . . . . . . . . . 56
3.4 Schematic representation of the algorithm . . . . . . . . . . . . . . . . . . . 57
IXX LIST OF FIGURES
3.5 Digitization of quantum jumps . . . . . . . . . . . . . . . . . . . . . . . . . 58
3.6 Second-order correlation function . . . . . . . . . . . . . . . . . . . . . . . . 59
3.7 Histogram of dwell times . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
3.8 Antibunching of quantum jumps . . . . . . . . . . . . . . . . . . . . . . . . 61
3.9 Quantum jumps of one and two atoms at the cavity edge. . . . . . . . . . . 62
3.10 Model for two atoms quantum jumps . . . . . . . . . . . . . . . . . . . . . . 63
3.11 Quantum jumps of two atoms: Analysis . . . . . . . . . . . . . . . . . . . . 64
3.12 The measurement sequence of normal-mode splitting . . . . . . . . . . . . . 66
3.13 Scanning the atom cavity coupling strength along the cavity axis . . . . . . 68
3.14 Coupling strength stability after switching off the probe laser . . . . . . . . 69
3.15 Stability of the coupling strength during the cavity frequency chirp . . . . . 70
3.16 Dynamics of the . . . . . . . . . . . . . . . . . . . . . . . 71
3.17 Atom-cavity coupling strength during the measurement of the normal-mode
splitting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
3.18 Normal-mode splitting of a single atom . . . . . . . . . . . . . . . . . . . . . 74
03.19 Atomic population transfer by the F =4¡!F =4 probe laser . . . . . . . 75
3.20 Providing a better localization of atoms by an additional trapping potential 79